Sea level rise is an indicator of the extent of the warming of the Earth’s climate as well as a major threat to the world’s coastal zones. The rate of the rise of the global mean sea level has been accelerating since the Industrial Revolution, reaching over 3 mm/yr at present. New technologies developed over the past 25 years have enabled great strides in monitoring global sea level with both spaceborne and in situ sensors, revealing information that is useful for understanding the phenomenon and predicting its evolution.

Introduction

Over the geological history of Earth, sea level has varied by hundreds of meters as a result of tectonic and climatic processes. The current ice age cycle started about 3 million years ago, with a 100,000-year cycle in the past 1 million years primarily caused by fluctuation in the Earth’s orbit around the Sun. During the most recent glacial maximum 25,000 years ago, sea level was about 130 meters below the present level. During the deglaciation that began 20,000 years ago, sea level began rising rapidly at 1 cm/year until 7,000 years ago, when the rate stabilized to 0.2 mm/yr (Carlson and Clark 2012). In the 20th century, however, the rate rose tenfold to 2 mm/yr and in the past 20 years it accelerated to 3 mm/yr, a third of the rate during the maximum deglaciation (Church and White 2011).

Causes and Impacts

The recent rise of the global sea level is caused by thermal expansion from the warming of the ocean and the melting of ice on land. During the past 20 years the former has accounted for about one third of the rise and the latter about two thirds according to the 5th Assessment Report of the Intergovernmental Panel on Climate Change (IPCC; Church et al. 2013). Based on the high end of the projected warming of the planet in the coming decades (compared with the period of 1986–2005), the IPCC estimated the rise of the global mean sea level (GMSL) at 52–98 cm by 2100, with a rate of 8–16 mm/year during 2081–2100.

The rising GMSL has already significantly affected the 10 percent of the world’s population living at elevations lower than 10 m near the ocean. The threats to low-lying islands of the Maldives and the coastal zones of Bangladesh are well known. In New York City the last 7 percent of the storm surge from Hurricane Sandy affected 11.4 percent more people and 11.6 percent more housing units, and caused 24 percent more total property damage, than it would have without the sea level rise of the past 100 years (Leifert 2015). The higher sea level makes many coastal cities prone to flooding during high tides and increases the frequency of so-called nuisance floods (e.g., Kruel 2016).

Evolution of Efforts to Measure Sea Level Rise

Before the advent of satellite remote sensing and its global coverage, it was not straightforward to measure the GMSL using only tide gauges, whose sparse and uneven coverage resulted in unknown sampling errors in efforts to determine the GMSL. In the late 1960s the concept of using a radar altimeter on an Earth-orbiting satellite to measure sea surface height was developed, and the first such altimeter, launched in the 1970s, demonstrated space observations of sea level. Within two decades the accuracy and precision of satellite altimetry were sufficient to determine the GMSL and small changes in it.

Two other advances important to understanding changes in the GMSL emerged in the 1990s. One was the deployment of autonomous profiling floats in the ocean to measure the temperature and salinity of the water column globally through an international program called Argo.[1] The technique enables determination of water density as a function of depth and its effects on changes in sea level. For example, rising temperature would raise sea level via thermal expansion.

The other development was the launch of satellites to measure Earth’s changing field of gravity resulting from the changing distribution of mass near the planet’s surface. This satellite mission, called GRACE (Gravity Recovery and Climate Experiment[2]), has determined the contribution of changes in the mass of the water column to sea level change.

Together, satellite altimetry, Argo, and GRACE provide an observing system for determining changes in the global sea level and their causes: changes in water density and mass. The resulting information has revolutionized both the capability to monitor small signs of global sea level rise and understanding of the physical processes needed to project future changes.

Satellite Altimetric Measurement of Sea Level Change

The measurement configuration of satellite altimetry is illustrated in figure 1. A radar altimeter on an orbiting satellite, operating at microwave frequencies of 10–35 GHz, sends short pulses to the sea surface and receives the return signals, and the round-trip travel time is used to determine the distance between the satellite and sea surface. With the height of the satellite relative to Earth’s center of mass (~1,000 km) determined by the technology of precision orbit determination, it is possible to calculate the geocentric sea level (the height of sea surface relative to Earth’s center of mass).

Figure 1

The shape of the sea surface is dictated to a large extent by the variation of Earth’s gravity field at its surface, caused by the uneven structure and density of the lithosphere, the upper layer of solid earth. The relief of the sea surface is within a couple of meters of a surface of constant gravity, called the geoid, whose relief relative to the reference ellipsoid has a range of about 200 m. The deviation of the sea surface from the geoid is called the ocean dynamic topography.[3]

Early Efforts

The first spaceborne radar altimeter was aboard the Skylab missions in the early 1970s (Krishen 1975), followed by the series of the Geodetic Earth Orbiting Satellite (GEOS) missions (Stanley 1979) in the mid-1970s to refine the measurement to an accuracy necessary to determine the shape of the geoid to a few meters. Not until the launch of Seasat in 1978 (Born et al. 1979) was the accuracy of satellite altimetry sufficient—within a few centimeters—for measuring the variability of ocean surface topography; the uncertainty of the satellite’s radial height was about 1 m over scales of 10,000 km.

Motivated by the desire to determine the ocean general circulation at the scales of the ocean basin, a satellite mission called TOPEX/Poseidon (T/P) was developed jointly by NASA and the French space agency, CNES (Fu et al. 1994). Launched in 1992, T/P was able to measure the ocean dynamic topography and geocentric sea level to centimetric accuracy, representing a remarkable achievement in improving the capability of satellite altimetry by a factor of 100 in 25 years.[4]

Increased Accuracy

A series of satellite missions carrying radar altimeters has been on orbit since the 1990s, yielding a continuous record of global sea level and ocean dynamic topography. Although the early mission development was not focused on the GMSL, whose required accuracy was too daunting a task in the 1980s, the breakthrough enabled by T/P has made the GMSL a key objective of current altimetry missions.

Figure 2

A time series shows the change of the GMSL from 1993 to 2018 (figure 2; Nerem et al. 2018). The record is the result of extensive calibration and validation on four missions (T/P and its follow-on Jason series). The GMSL during this period is estimated at 3.1 ± 0.4 mm/yr (the uncertainty is largely from calibration against the global tide gauge network). Other studies have placed the uncertainty at 0.3–0.5 mm/yr (Ablain et al. 2017). Before satellite measurement, it was not possible to rigorously estimate the GMSL and its uncertainty.

How good is the current capability of determining the rate of GMSL rise? The rate of acceleration to reach 70 cm rise above today’s GMSL by 2100 (roughly the middle of the IPCC’s high-end projection) is ~0.1 mm/yr2. The recent study by Nerem and colleagues (2018) concluded, with high statistical confidence, that acceleration of this magnitude—0.08 mm/yr2—is already observed in the present 25-year record of altimetric GMSL. This finding suggests that the current capability of monitoring the GMSL meets society’s needs for rigorous assessment of future threats of global sea level rise.

Argo Float Measurement of Heat-Induced Sea Level Change

The profiling float (figure 3) is a free-drifting and -wholly autonomous ocean instrument developed by Davis and colleagues (2001) for research use during the 1990s World Ocean Circulation Experiment. The instruments adjust their buoyancy and hence their depth by pumping mineral oil between a reservoir in the float’s pressure case and an external -bladder. Changes in the volume of a float by a few percent cause buoyancy variation sufficient to keep the float on the sea surface, make it neutrally buoyant at intermediate depths, or send it to the ocean bottom. A sensor package mounted on top of the float collects profile measurements of temperature, salinity, and pressure. The float cycles between the sea surface and a depth of 2,000 m every 10 days, transmitting its GPS position and profile data via Iridium satellites when it surfaces.

Figure 3

Before the development of profiling floats, subsurface ocean temperature data could be collected only when a ship was present or from fixed-point moorings. Resulting datasets were very sparse and irregular in space and time, with most data obtained in the Northern Hemisphere, near continents, and in summer. The profiling float was a revolutionary instrument for oceanography because it provides high-quality data anywhere, any time.

In 1997 an international group of scientists proposed the installation of a global array, named Argo, consisting of 3,300 profiling floats (Argo Science Team 1998). A primary motivation was to assess climate variability and change, including GMSL rise due to ocean warming. The first Argo floats were deployed in 1999; by 2007 there were over 3,000 distributed globally, and about 3,800 have been maintained for the past decade. Begun in 2006 as a multinational effort, Argo is sustained by national programs in more than 25 countries (figure 4).

Figure 4

Recent advances in profiling float and sensor technologies now make it possible to sample to the ocean bottom at depths of up to 6,000 m (Deep Argo; Zilberman 2017) and to sample additional parameters such as dissolved oxygen, nitrate, pH, and biooptical properties (Biogeochemical Argo; Johnson et al. 2009). The global Argo array greatly increases the accuracy of the earlier estimates of thermosteric GMSL rise based on the sparse pre-Argo datasets.

The thermal expansion coefficient for seawater -varies with temperature and pressure. The top 1,000 m of seawater at the equator, if warmed uniformly by 0.1°C, would expand in height by 1.8 cm, while at 60°S the expansion would be 0.8 cm. Sea-Bird electronic sensors on Argo floats measure temperature, salinity, and pressure with high accuracy (.002°C, .01 psu, and 0.1 percent respectively). Given the sensor accuracy and the fact that float-to-float differences are mostly random, errors in large-scale temperature variability are mainly due to the array’s spatial coverage (figure 4). That is, limited data coverage in the deep ocean and spatial inhomogeneity are the main source of error in thermosteric GMSL estimates. Deep ocean warming below Argo’s present depth limit of 2,000 m is estimated to account for 0.1 mm/yr to GMSL rise in 1993–2010 (Purkey and Johnson 2010), or about 10 percent of the 0–2,000 m GMSL thermosteric contribution, which was 1.0 ± 0.2 mm/yr in 2004–16 (Thompson et al. 2017).

The Argo program has produced over 12 years of global data, which are freely available via the internet (www.argo.net) in near real time and as research quality after 1 year. A monthly interpolated version (Roemmich and Gilson 2009) is used to estimate the trend in steric height of the sea surface relative to 2,000 decibars as a function of location (figure 5). The same calculation is made over the same time interval with satellite altimetric sea level data.

Figure 5

Global patterns of the trend in altimetric sea surface height and steric height are compared in figure 5. Two aspects of this comparison are evident. First, the global mean of the altimetric height trend (upper panel, 3.3 mm/yr) is greater than that of steric height (lower panel, 1.3 mm/yr), and this 2 mm/yr difference is attributable to mass (discussed below). Second, discounting the difference in global means, the pattern of regional variability in the altimetric and steric height trends is similar, indicating that the mass trend, while large, is more spatially uniform than the steric height trend.

Regional trends in steric height (figure 5) can be much larger than the global mean.[5] These massive redistributions of warm ocean water are largely wind driven and can increase the rate of sea level rise regionally for years or longer; some regions of large steric sea level rise, such as along 40°S, are known to have multidecadal timescales (Roemmich et al. 2016). In other cases the warm anomalies represent interannual -changes that appear trend-like in the 12-year time series; for example, the large maximum in the eastern equatorial Pacific is attributable to a major El Niño episode in 2015–16. A longer Argo time series is needed for effective separation of interannual and decadal variability.

GRACE Measurement of Mass-Induced Sea Level Change

The original concept of determining the ocean circulation from space required not only satellite altimetry but also the measurement of the geoid for computing the ocean dynamic topography. After many variations of the design of a spaceborne gravity mission, the concept of GRACE emerged to measure the minute change of gravity experienced by two spacecraft on orbit tracking each other using a microwave link (NRC 1997). GRACE can determine not only the near surface gravity field of Earth but also its change with time.

How GRACE Works

Figure 6

To be sensitive to the spatial variability of Earth’s gravity associated with the structure and density of the upper layers of the solid earth, the two GRACE spacecraft, launched in 2002, were placed in a near-Earth orbit of ~500 km, 220 km apart (figure 6). GRACE measures a “biased range” between the two spacecraft by tracking the carrier phase of a K and Ka band microwave signal (Tapley et al. 2004). The bias is constant over long periods so that the range change is very accurately measured. The wavelength of the K/Ka signals is about 1 cm. Careful design and averaging over several seconds yield accuracy between 1 part per thousand and 1 per ten thousand of the wavelength, corresponding to a few microns in range every 5 seconds. The data are often processed as range rate, which is good to about 0.1 µm/sec for 5-second averages. Since the measurements are one way from each spacecraft, it is important to know the time of transmission and reception on each spacecraft and to be able to synchronize those to about 100 picoseconds. The accuracy of GRACE in measuring the change of gravity can be expressed as that associated with the mass of water of 1–2 cm thickness over a circle with a radius of 300 km (Landerer and Swenson 2012).

Uses of GRACE Data

The gravity measurement of GRACE enables determination of the change of mass over large ocean areas and, when integrated globally, GRACE data reveal the contributions of ice melt in the change of the GMSL. As shown in figure 7, the combination of the steric sea -level change (caused by the change of ocean density), estimated from the Argo data, with the barystatic sea level change (caused by the change of ocean mass) matches the altimetry measurement of total sea level change fairly well. The synergy of the three measurement systems creates an opportunity for cross-validation of the difficult and important measurement of the GMSL, which is an indicator of both the extent of climate change and impacts on humans.

Figure 7

GRACE data have revealed the rate of the melting of ice sheets on Greenland and Antarctica (Velicogna 2009), whose potential massive breakup and melting are the primary sources of the looming threat of sea level rise. The fragile West Antarctic Ice Sheet holds enough water to raise the GMSL by 5 m, in contrast to the 0.5 m -capacity of the warming of the ocean. Distribution of the melt water will be uneven geographically, because of changes both in Earth’s gravity due to the massive ice loss in the polar regions and in the ocean’s density and circulation due to climate change. The greatest magnitude is projected to account for 20 percent of the change of the GMSL (Slangen et al. 2012). Such variability in regional sea level change is of great concern in efforts to plan for coastal adaptation. Figure 8 displays the 2005–14 pattern of sea level change due to the melting of polar ice sheets estimated from the GRACE data (Adhikari and Ivins 2016), qualitatively similar to the projection of Slangen and colleagues, given the relatively short data record.

Figure 8

An interesting feature is that the reduced gravity caused by the mass loss of the polar ice sheets has caused sea level to fall in regions close to the source of the melting in Greenland and Antarctica and rise elsewhere. As opposed to the interannual pattern of sea level change shown in figure 5, the pattern of change from ice melting has a much longer time scale, which is most relevant to coastal planning and decision making.

Concluding Remarks

Advances in technology for observing the ocean from spaceborne and in situ sensors make it possible to monitor the rise of the global sea level with unprecedented accuracy.

Signs of accelerating GMSL rise over the past two decades have been detected by the satellite radar altimetry system with high statistical confidence. The priority of the international space community is to maintain the present capability to monitor current and future changes. Spaceborne gravity measurement allows detection of changes in GMSL from water mass exchange between the ocean and the rest of Earth, primarily from ice melting. The in situ float system detects changes in water temperature and salinity, and hence density, with the long-term trend primarily due to the warming of the climate.

The various systems together not only provide information to understand the causes of sea level rise but also enable cross-checking for consistency to ensure the accuracy of the observations, which are critical for dealing with climate change.

[3] The horizontal gradient of the dynamic topography is proportional to the part of ocean surface circulation that is balanced by the Earth’s rotation (the Coriolis force). This flow component, the geostrophic circulation, is responsible for the large-scale transport of ocean mass and heat, providing a fundamental motivation for the development of satellite altimetry in addition to the determination of sea level.

[4] The tremendous progress of satellite altimetry is described in Fu and Cazenave (2001) and Stammer and Cazenave (2018).

[5] Changes in global mean steric height due to salinity are too small to detect in the 12-year time series, but there are -regional examples, particularly at high latitude where the impact of -salinity on steric height is significant.